The vertex of the parabola is given by :
[tex]\displaystyle{ ( \frac{-b}{2a}, f(\frac{-b}{2a}) )[/tex].
So, [tex]\displaystyle{ \frac{-b}{2a}[/tex] is the first coordinate of the vertex, which means it is also the point where the line of symmetry passes.
The line of symmetry divides the parabola into 2 symmetrical parts: the x-intercepts are also symmetrical to each other with respect to this line.
So, if one of the x-intercepts is [tex]\displaystyle{ (\frac{-b}{2a}+3, 0)[/tex], that is 3 units to the right of the x-intercept, the other must be 3 units to the left. Thus, the second x-intercept is :
Answer: [tex]\displaystyle{ (\frac{-b}{2a}-3, 0)[/tex],
